Chapter 2: Graphs, Charts, and Tables--Describing Your Data

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74 CHAPTER 2 • GRAPHS, CHARTS, AND TABLES—DESCRIBING YOUR DATA SUMMARY Constructing Line Charts A line chart, also commonly called a trend chart, is developed using the following steps: 1. Identify the time-series variable of interest and determine the maximum value and the range of time periods covered in the data. 2. Construct the horizontal axis for the time periods using equal spacing between each time period. Construct the vertical axis with a scale appropriate for the range of values of the time-series variable. 3. Plot the points on the graph and connect the points with straight lines. EXAMPLE 2-10 Line Charts Grogan Builders Grogan Builders produces mobile homes in Alberta, Canada. The owners are planning to expand the manufacturing facilities. To do so requires additional financing. In preparation for the meeting with the bankers, the owners have assembled data on total annual sales for the past 10 years. These data are shown as follows: 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 1,426 1,678 2,591 2,105 2,744 3,068 2,755 3,689 4,003 3,997 TRY PROBLEM 2.46 The owners wish to present these data in a line chart to effectively show the company’s sales growth over the 10-year period. To construct the line chart, the following steps are used: Step 1 Identify the time-series variable. The time-series variable is units sold measured over 10 years, with a maximum value of 4,003. Step 2 Construct the horizontal and vertical axes. The horizontal axis will have the 10 time periods equally spaced. The vertical axis will start at zero and go to a value exceeding 4,003. We will use 4,500. The vertical axis will also be divided into 500-unit increments. Step 3 Plot the data values on the graph and connect the points with straight lines. Mobile Homes Sold 4,500 4,000 3,500 3,000 2,500 2,000 1,500 1,000 500 0 Grogan Builders Annual Sales 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 Year
CHAPTER 2 • GRAPHS, CHARTS, AND TABLES—DESCRIBING YOUR DATA 75 CHAPTER OUTCOME #7 Scatter Diagram A two-dimensional graph of plotted points in which the vertical axis represents values of one quantitative variable and the horizontal axis represents values of the other quantitative variable. Each plotted point has coordinates whose values are obtained from the respective variables. Dependent Variable A variable whose values are thought to be a function of, or dependent on, the values of another variable called the independent variable. On a scatter plot, the dependent variable is placed on the y axis and is often called the response variable. Independent Variable A variable whose values are thought to impact the values of the dependent variable. The independent variable, or explanatory variable, is often within the direct control of the decision maker. On a scatter plot, the independent variable, or explanatory variable, is graphed on the x axis. Scatter Diagrams In Section 2.1 we introduced a set of statistical tools known as joint frequency distributions that allow the decision maker to examine two variables at the same time. Another tool used to study two quantitative variables simultaneously is the scatter diagram, or the scatter plot. There are many situations in which we are interested in understanding the bivariate relationship between two quantitative variables. For example, a company would like to know the relationship between sales and advertising. A bank might be interested in the relationship between savings account balances and credit card balances for its customers. A real estate agent might wish to know the relationship between the selling price of houses and the number of days that the houses have been on the market. The list of possibilities is almost limitless. Regardless of the variables involved, there are several key relationships we are looking for when we develop a scatter diagram. Figure 2.20 shows scatter diagrams representing some key bivariate relationships that might exist between two quantitative variables. Chapters 14 and 15 make extensive use of scatter diagrams. They introduce a statistical tool called regression analysis that focuses on the relationship between two variables. These variables are known as dependent and independent variables. PERSONAL COMPUTERS Can you think of any product that has increased in quality and capability as rapidly as personal computers? Not that long ago an 8-MB RAM system with a 486 processor and a 640-K hard drive sold in the mid-$2500 range. Now the same money would buy a 3.0 GHz or faster machine with a 100 GB hard drive and 512-MB RAM or more! In September 2005 we examined various Internet Web sites looking for the best prices on personal computers. The data file called Personal Computers contains data on several characteristics, including processor speed, hard drive capacity, RAM, whether a monitor is included, and the price for 13 personal computers. Of particular interest is the relationship between the computer price and processing speed. Our objective is to develop a scatter diagram to graphically depict what, if any, relationship exists between these two variables. The dependent variable is price and the independent variable is processor speed. Figure 2.21 shows the Excel scatter diagram output. The relationship between processor speed and price is somewhat curvilinear and positive. FIGURE 2.20 Scatter Diagrams Showing Relationships Between x and y y y y (a) Linear x (b) Linear x (c) Curvilinear x Excel and Minitab Tutorial y y y (d) Curvilinear x (e) No Relationship x (f) No Relationship x
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Chapter 2: Graphs, Charts, and Tables--Describing Your Data

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